Questions

1) What is the ordered pair for point E in rectangle CDEF in terms of “a” and/or “b”?

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2) What is the ordered pair for point H in parallelogram GHIJ?

a.) (a, c)

b.) (a + c, b)

c.) (a – c, b)

d.) (a, 0)

3) What is the ordered pair for point E in equilateral triangle DEF? State the letter of the correct answer.

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4) What is the ordered pair for point V in isosceles trapezoid TUXY?

a.) (a, c)

b.) (a + c, b)

c.) (c – a, b)

d.) (c – a, 0)

5) Read and study the information and the figure shown below to answer the following questions: (a) What is the ordered pair for midpoint M? (b) In terms of “a” and “b”, what is the length of segment MQ? (c) In terms of “a” and “b”, what is the length of segment MR? (d) In terms of “a” and “b”, what is the length of segment MS?

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6) Based on the information collected in the previous problem, justify the following statement: “The midpoint of the hypotenuse of a right triangle is the center of a circle circumscribed about it”.

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7) Answer the following questions for Proof 1: (a) What are the coordinates of point M? (b) What are the coordinates of point N? (c) What is the slope of segment BC? (d) What is the slope of segment MN? (e) What is the slope of segment AD?

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8) Use the information collected in the previous problem to justify the following statement: “The segment formed by the midpoints of the nonparallel sides is parallel to the bases of the trapezoid”.

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9) Answer the following questions for Proof 2: (a) What is the length of segment MN? (b) What is the length of segment BC? (c) What is the length of segment AD? (d) What is the sum of the lengths of segments AD and BC?

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10) Use the information collected in the previous problem to justify the following statement: “The length of the segment formed by the midpoints of the nonparallel sides of a trapezoid is half the length of the sum of the bases of the trapezoid”.

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11) What is the term used to indicate a one-to-one correspondence between the points that make up a transformation from a pre-image to an image?

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12) True or False. Points A and L are corresponding vertices, points B and M are corresponding vertices, points C and N are corresponding vertices, and points D and O are corresponding vertices.

True

False

13) Which statement is a symbolic statement of a translation that indicates triangle JKL is the pre-image? State the letter of the correct answer.

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14) Fill in the blanks for the following statements about the mapping shown below: (a) Point H maps onto point _____. (b) Point I maps onto point _____. (c) Point J maps onto point _____. (d) Point K maps onto point _____.

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15) What is the pre-image of angle RSQ shown in the figure below? State the letter of the correct answer.

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16) Fill in the blank: A transformation that maps every segment in a plane to a congruent segment is a(n) _________.

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17) What are the lengths of (a) QR and DE, (b) TS and GF, (c) RS and EF, and (d) QT and DG?

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18) True or False: The mapping of parallelogram QRST to parallelogram DEFG is an isometry.

True

False

19) Which image is the isometric image of trapezoid ABCD? State the letter of the correct answer.

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20) Which ratio(s) simplifies to 1/2?

a.) CD : JK

b.) DE : KL

c.) CE : JL

d.) all of the above

21) True or False: The mapping shown below is a similarity transformation.

True

False

22) The figure below shows segment JK as a reflection of segment CD over the y-axis. The five points that are enlarged on each segment are corresponding points. Print out and complete each table by filling in the coordinates for the five designated points. Compare the x-coordinate and y-coordinate of the points on segment CD (pre-image) with the x-coordinate and y-coordinate of the points on segment JK (image). Complete the following rule that would pertain to all reflections over the y-axis: For images reflected over the y-axis, if the pre-image coordinates are designated as (x, y), then the image of (x, y) is (____, ____).

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23) True or False: The transformation shown below is a translation.

True

False

24) In the figure below, pre-image ABCD is translated to image A'B'C'D'. Which statement reflects the notation in the coordinate plane? State the letter of the correct answer.

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25) Which notation describes the translation of the sailboat B(70, 20) to the lighthouse B'(10, 80) as a change in (x, y)?

a.) (x, y) ==> (x + 60, y – 60)

b.) (x, y) ==> (x – 60, y + 60)

c.) (x, y) ==> (x – 60, y – 60)

d.) (x, y) ==> (x + 60, y + 60)

26) The vertices of a quadrilateral are J(–4, 0), K(–2, 5), L(1, 1), M(–2, –2). Print out the figure of the pre-image shown below and graph the translation naming the image, J’K’L’M’. What are the coordinates of each of the new vertices of the image?

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27) True or False: The transformation shown below is a reflection.

True

False

28) Identify the line of reflection in the figure shown below?

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29) Answer the following questions about the reflection shown below: (a) Point B is a reflection of point _____. (b) Point J is a reflection of point _____. (c) Angle ABC is a reflection of angle ____ over line “l”.

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30) The coordinates of the endpoints of line segment CD are C(–4, 1) and D(3, 4). Reflect the line segment over the x-axis. (a) State the coordinates of the image of the endpoints of segment C'D'. (b) Write a rule that would pertain to all points reflected over the x-axis.

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31) Reflect point C over the line, y = –2, and name it point C’. Reflect point C’ over the line, y = 2, and name it point C’’. What is the location of C’’?

a.) C’’(3, 0)

b.) C’’(3, 2)

c.) C’’(3, 4)

d.) C’’(3, 6)

32) Which parts of the kite are symmetrical? Select the BEST answer.

a.) top right triangles of the kite

b.) bottom right triangles of the kite

c.) the triangles that represent the bows

d.) all of the above

33) In reflection symmetry, a “point of symmetry” is a midpoint for all segments that pass through it and have endpoints on a figure. Which figure does NOT display a “point of symmetry” in reflection symmetry?

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34) True or False: The transformation shown below is a rotation.

True

False

35) In the figure below, pre-image trapezoid Z is rotated about point X to image trapezoid Z’. Rotations can be derived from two reflections. Explain how this same transformation can be made by completing two reflections. A faint dotted trapezoid is provided to help with the explanation.

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36) In the figure shown below, a 70-degree angle is formed by lines “s” and “t”, the lines of reflection. What is the angle of rotation that transformed pre-image R to image R’ around point Q.

a.) 35 degrees

b.) 70 degrees

c.) 105 degrees

d.) 140 degrees

e.) 175 degrees

37) Draw quadrilateral ABCD with vertices of A(–4, 0), B(–4, 4), C(–2, 3), and D(–2, –1). Rotate the quadrilateral 90 degrees clockwise around the origin and draw quadrilateral A’B’C’D’. What are the coordinates of each of the vertices in image A’B’C’D’? State the name of each vertex and the corresponding coordinates.

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38) In the figure shown below, pre-image AB is rotated 90 degrees counter-clockwise around the origin to image A’B’. Print out the tables provided below to write and compare the coordinates of the endpoints of segment AB and segment A’B’. Which rule represents a 90-degree counter-clockwise rotation around the origin in the coordinate plane? State the letter of the correct answer. (Note: “P(x, y)” is the general notation of the name of a pre-image’s point and its coordinates. “P’(x, y)” represents the general notation of the name of an image’s point and its coordinates.

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39) Describe how to create Figure 2 from Figure 1.

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40) In the figure below, segment JK is a dilation of segment GH with respect to point Q as the center of dilation and a scale factor of 1/2. State the letter of the correct statements about the figure.

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41) In the figure below, segment AB is a dilation of segment CD with respect to point Q as the center of dilation. The length of segment QC is 5 and the length of segment CA is 10. What scale factor was used to create the dilation?

a.) 2

b.) 3

c.) 1/2

d.) 1/3

42) In the figure below, hexagon A'B'C'D'E'F’ is the image of ABCDEF after a dilation. What is the scale factor?

a.) 1

b.) 2

c.) 3

d.) 4

43) In the figure below, triangle RST is a dilation of triangle JKL with the center of dilation at point P. What is the scale factor?

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44) Compare the lengths of the image (larger picture) and its dilation (smaller picture). What is the scale factor?

a.) 1/2

b.) 1/3

c.) 2/3

d.) 3/4

45) The vertices of four-point star ABCD are A(–2, 0), B(–4, 2.5), C(–2, 5), and D(0, 2.5). Find and write the coordinates of the vertices of image, A’B’C’D', after a dilation of a scale factor, k = 2, with respect to the origin as the center of dilation.

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46) Dilate parallelogram PQRS by a scale factor of 0.6 with point P as the center of dilation. The length of segment RS is 4.8 cm and the length of segment QR is 10.8 cm. P and P' are the same point. (a) What is the length of PQ’? (b) What is the length of S’R’? (c) What is the length of Q’R’? (d) What is the length of PS’?

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